triangle AOB is a right angled triangle....(1.5, 2)is the midpoint co-ordinate of AB the co-ordinate of B is (2.5. 0)...
Find the height of point A reached by the the top of the triangle...
Could you show this step-by step please?
To find the height of point A reached by the top of the triangle, we can use the midpoint formula.
Step 1: Find the coordinates of point A
Since (1.5, 2) is the midpoint of AB, we can use the midpoint formula to find the coordinates of point A. The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's substitute the given values:
(1.5, 2) = ((x1 + 2.5) / 2, (y1 + 0) / 2)
Simplifying, we get:
1.5 = (x1 + 2.5) / 2
2 = y1 / 2
Solving these equations, we find:
x1 + 2.5 = 3
x1 = 0.5
y1 = 4
Therefore, the coordinates of point A are (0.5, 4).
Step 2: Calculate the height of point A
Since triangle AOB is a right-angled triangle, we can use the distance formula to find the height of point A. The distance formula is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given values:
Distance = √((2.5 - 0.5)^2 + (0 - 4)^2)
Distance = √(2^2 + (-4)^2)
Distance = √(4 + 16)
Distance = √20
Simplifying, we get:
Distance ≈ 4.47
Therefore, the height of point A reached by the top of the triangle is approximately 4.47 units.